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Simplifying 22x2 + 11x = 5 Reorder the terms: 11x + 22x2 = 5 Solving 11x + 22x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 11x + 22x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 11x + 22x2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -0.2272727273 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.5x + 0.2272727273 + x2 = 0 + 0.2272727273 Reorder the terms: -0.2272727273 + 0.2272727273 + 0.5x + x2 = 0 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.2272727273 0.5x + x2 = 0 + 0.2272727273 Combine like terms: 0 + 0.2272727273 = 0.2272727273 0.5x + x2 = 0.2272727273 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.2272727273 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.2272727273 + 0.0625 Combine like terms: 0.2272727273 + 0.0625 = 0.2897727273 0.0625 + 0.5x + x2 = 0.2897727273 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.2897727273 Calculate the square root of the right side: 0.538305422 Break this problem into two subproblems by setting (x + 0.25) equal to 0.538305422 and -0.538305422.Subproblem 1
x + 0.25 = 0.538305422 Simplifying x + 0.25 = 0.538305422 Reorder the terms: 0.25 + x = 0.538305422 Solving 0.25 + x = 0.538305422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.538305422 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.538305422 + -0.25 x = 0.538305422 + -0.25 Combine like terms: 0.538305422 + -0.25 = 0.288305422 x = 0.288305422 Simplifying x = 0.288305422Subproblem 2
x + 0.25 = -0.538305422 Simplifying x + 0.25 = -0.538305422 Reorder the terms: 0.25 + x = -0.538305422 Solving 0.25 + x = -0.538305422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.538305422 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.538305422 + -0.25 x = -0.538305422 + -0.25 Combine like terms: -0.538305422 + -0.25 = -0.788305422 x = -0.788305422 Simplifying x = -0.788305422Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.288305422, -0.788305422}
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